Many biological, epidemiological and medical studies (both animal and human) have as an outcome, or response of interest, one (or more) event time(s), the time from some appropriate starting point until some event of interest (such as the occurrence of a particular symptom or disease, remission, relapse, death due to some specific disease, or simply death) occurs. The overall theme of this research is to assess the effects of covariates, or potential risk factors, on event times in complex biomedical studies. The first specific aim is to study the relationships of various demographic variables, environmental factors and/or treatment modalities on disease process or mortality where individuals in subgroups (such as siblings, litter mates, or spouses) are associated or where multiple events are recorded on the same individual. These events may occur or may not occur during the duration of the follow-up (i.e., censoring has occurred). The investigators intend to build upon their experience with frailty models to investigate novel ways to incorporate frailties into multivariate survival analysis. These models will include examining the introduction of correlated individual frailties as opposed to a shared frailty for each member of the unit. The investigators plan on using data from the International Bone Marrow Transplant Registry (IBMTR) and the North American Autologous Bone Marrow Transplant Registry (NAABMTR) to provide an immediate application of the methods to be developed in this proposal. The IBMTR is an international study group engaged in ongoing investigation of allogeneic and syngeneic bone marrow transplantation for the past 20 years. The IBMTR database contains detailed information for more than 16,600 patients transplanted for more than 80 diseases at 278 centers worldwide (68% of all teams in the world performing allogeneic bone marrow transplants participate in this registry). Since the proportional hazards assumption is not always appropriate, a second specific aim of this study is to study alternatives to the proportional hazards model. Models which will be studied in this proposal include the accelerated failure time model and the additive hazards model. Since there is usually uncertainty in deciding which model is most appropriate, goodness of fit methods for these models will be studied so as to provide guidance to investigators in making these decisions. Finally, randomized studies are not always available to make comparisons between registry data and patients treated in a prospective clinical trial. For example, in transplantation studies, such controls cannot be obtained because large-scale randomized clinical trials are not available and the analysis must rely on historical controls or controls from prospective studies of alternative therapy. Still interest centers on answering questions like "How does this treatment regime compare to a more conservative one?" or "Have patients returned back to normal, after an appropriate recovery period with respect to projected survival?" Because the answers to such questions will depend heavily on potential prognostic factors, a third specific aim is to develop methodology to answer these questions accommodating such adjustments. For all the above methods developed a study of both large and small sample properties will be carried out. This is crucial since not all studies are large enough for the asymptotic properties to be applicable. Attention will also be given to assessing model fit. Finally, software will be written to implement the statistical methods developed.